"We are experiencing higher than normal call volume. ..."
If this quote sounds familiar to you, you are definitely not alone. I'm confronted with it almost daily. In most cases, the message is very generic without any indication of how long you are able to wait or at what part of the queue your call is in.
What kind of user experience is this? Not all waits are created equal. If you're thinking of waiting for a table at a restaurant, you're usually able to judge how long the wait is. The question is so common that the hostess will normally give you this information automatically. With the knowledge of a wait time, you're able to make an informed decision whether the wait will be justified or not.
On the phone however, this is not always so obvious. If you want to ask a quick question, you might be willing to wait up to 5 minutes. But you're not sure how long the wait is. You might want to risk the 5 minutes and if you're still on hold, your mindset may change in the fact that since you already spent 5 minutes waiting, you might as well wait some more. If you don't, those 5 minutes went completely to waste.
On the other hand, if you knew the amount of expected wait time, you might choose to call back at another less busy time. As an added bonus, this would even benefit the company you are calling as people who don't have urgent matters may not be inclined to wait and jam the phone lines, with less cost to the company as well.
Basically, being able to communicate an expected wait time would increase efficiency and the user experience for all parties involved. It should be noted that there are some companies that have started to implement estimated wait times. Unfortunately though it seems like the majority of call centers out there do not.